import math
import torch
from torch.optim.optimizer import Optimizer

from .types import Betas2, OptLossClosure, Params, State, OptFloat


__all__ = ('AdaBound',)


class AdaBound(Optimizer):
    r"""Implements AdaBound algorithm.

    It has been proposed in `Adaptive Gradient Methods with Dynamic Bound of
    Learning Rate`__.

    Arguments:
        params: iterable of parameters to optimize or dicts defining
            parameter groups
        lr: learning rate (default: 1e-3)
        betas: coefficients used for computing running averages of gradient
            and its square (default: (0.9, 0.999))
        final_lr: final (SGD) learning rate (default: 0.1)
        gamma: convergence speed of the bound functions
            (default: 1e-3)
        eps: term added to the denominator to improve numerical stability
            (default: 1e-8)
        weight_decay: weight decay (L2 penalty) (default: 0)
        amsbound: whether to use the AMSBound variant of this algorithm

    Example:
        >>> import torch_optimizer as optim
        >>> optimizer = optim.AdaBound(model.parameters(), lr=0.1)
        >>> optimizer.zero_grad()
        >>> loss_fn(model(input), target).backward()
        >>> optimizer.step()

    __ https://arxiv.org/abs/1902.09843
    """

    def __init__(
        self,
        params: Params,
        lr: float = 1e-3,
        betas: Betas2 = (0.9, 0.999),
        final_lr: float = 0.1,
        gamma: float = 1e-3,
        eps: float = 1e-8,
        weight_decay: float = 0,
        amsbound: bool = False,
    ) -> None:
        if lr <= 0.0:
            raise ValueError('Invalid learning rate: {}'.format(lr))
        if eps < 0.0:
            raise ValueError('Invalid epsilon value: {}'.format(eps))
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError(
                'Invalid beta parameter at index 0: {}'.format(betas[0])
            )
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError(
                'Invalid beta parameter at index 1: {}'.format(betas[1])
            )
        if final_lr < 0.0:
            raise ValueError(
                'Invalid final learning rate: {}'.format(final_lr)
            )
        if not 0.0 <= gamma < 1.0:
            raise ValueError('Invalid gamma parameter: {}'.format(gamma))
        if weight_decay < 0:
            raise ValueError(
                'Invalid weight_decay value: {}'.format(weight_decay)
            )
        defaults = dict(
            lr=lr,
            betas=betas,
            final_lr=final_lr,
            gamma=gamma,
            eps=eps,
            weight_decay=weight_decay,
            amsbound=amsbound,
        )
        super(AdaBound, self).__init__(params, defaults)
        self.base_lrs = [group['lr'] for group in self.param_groups]

    def __setstate__(self, state: State) -> None:
        super(AdaBound, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault('amsbound', False)

    def step(self, closure: OptLossClosure = None) -> OptFloat:
        r"""Performs a single optimization step.

        Arguments:
            closure: A closure that reevaluates the model and returns the loss.
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group, base_lr in zip(self.param_groups, self.base_lrs):
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                if grad.is_sparse:
                    msg = (
                        'AdaBound does not support sparse gradients, '
                        'please consider SparseAdam instead'
                    )
                    raise RuntimeError(msg)
                amsbound = group['amsbound']

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p)
                    if amsbound:
                        # Maintains max of all exp. moving avg. of
                        # sq. grad. values
                        state['max_exp_avg_sq'] = torch.zeros_like(p)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                if amsbound:
                    max_exp_avg_sq = state['max_exp_avg_sq']
                beta1, beta2 = group['betas']

                state['step'] += 1

                if group['weight_decay'] != 0:
                    grad = grad.add(group['weight_decay'], p.data)

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                if amsbound:
                    # Maintains the maximum of all 2nd moment running
                    # avg. till now
                    torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                    # Use the max. for normalizing running avg. of gradient
                    denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                else:
                    denom = exp_avg_sq.sqrt().add_(group['eps'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                step_size = (
                    group['lr']
                    * math.sqrt(bias_correction2)
                    / bias_correction1
                )

                # Applies bounds on actual learning rate
                # lr_scheduler cannot affect final_lr, this is a workaround
                # to apply lr decay
                final_lr = group['final_lr'] * group['lr'] / base_lr
                lower_bound = final_lr * (
                    1 - 1 / (group['gamma'] * state['step'] + 1)
                )
                upper_bound = final_lr * (
                    1 + 1 / (group['gamma'] * state['step'])
                )
                step_size = torch.full_like(denom, step_size)
                step_size.div_(denom).clamp_(lower_bound, upper_bound).mul_(
                    exp_avg
                )

                p.data.add_(-step_size)
        return loss
